# Determining the Correct Sampling Frequency for Signal Sampling

## Understanding Sampling Frequency for Correct Signal Sampling

**Sampling frequency** is a crucial parameter in signal processing, especially when it comes to digital signal sampling. The sampling frequency determines how often a signal is sampled or digitized per unit time.

When sampling a continuous signal to convert it into a discrete signal, it is essential to ensure that the sampling frequency is high enough to capture all relevant information and avoid aliasing.

## The Nyquist-Shannon Sampling Theorem

**The Nyquist-Shannon sampling theorem** is a fundamental concept in signal processing that states the sampling frequency must be greater than twice the highest frequency component in the signal to avoid aliasing.

This means that the sampling frequency should be at least twice the frequency at which the signal changes significantly to accurately reconstruct the original signal from its sampled version.

## Applying the Sampling Theorem to the Given Signal

In the given scenario, we are presented with a signal x(0) and its Fourier Transform X(w) that contains frequency components. To determine the correct sampling frequency f, we need to consider the highest frequency component in the signal.

By examining the Fourier Transform X(w) provided in the data, we find that the highest frequency component is 21.7000. Therefore, to avoid aliasing and accurately sample the signal, the sampling frequency f should be greater than twice this frequency.

Based on this analysis, the correct value of the sampling frequency f for correct sampling of the signal x(0) is fs > 7000.